A function f has an inverse function, f -1, if and only if f is one-to-one. A quick test for a one-to-one function is the horizontal line test. If a horizontal line intersects the graph of the function in more than one place, the functions is NOT one-to-one.
2016-2017 Congruency, Similarity, Right Triangles, and Trigonometry – Answer Key 3 MAFS.912.G-CO.1.1 EOC Practice Level 2 Level 3 Level 4 Level 5 uses definitions to choose examples and non-examples uses precise definitions that are based on the undefined notions of point, line, distance along a line, and distance around a circular arc
example f, to refer to the function as a whole and use f(x) to refer to the output when the input is x. For example, when language is used correctly, a graph of the function f in the x, y-plane is the graph of the equation y = f(x) since we graph those points, and only those points, of the form (x, y) where the y-coordinates are equal to f(x).
Describe the transformation of f(x) = x2 represented by g. Then graph each function. a. g(x) = − — 1 STRUCTURE 2 x 2 b. g(x) = (2x)2 + 1 SOLUTION a. Notice that the function is of the form g(x) = −ax2, where a = 1— 2. So, the graph of g is a refl ection in the x-axis and a vertical shrink by a factor of 1— 2 of the graph of f. x y f g ... Domain of Composite Function. We must get both Domains right (the composed function and the first function used). Summary. "Function Composition" is applying one function to the results of another. (g º f)(x) = g(f(x)) , first apply f(), then apply g().